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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. XX, XXX 2019 1

Computation Resource Allocation and TaskAssignment Optimization in Vehicular FogComputing: A Contract-Matching Approach

Zhenyu Zhou, Senior Member, IEEE, Pengju Liu, Junhao Feng, Yan Zhang, Senior Member, IEEE,Shahid Mumtaz, Senior Member, IEEE, and Jonathan Rodriguez, Senior Member, IEEE

Abstract—Vehicular fog computing (VFC) has emerged as apromising solution to relieve the overload on the base stationand reduce the processing delay during the peak time. Thecomputation tasks can be offloaded from the base station tovehicular fog nodes by leveraging the under-utilized computationresources of nearby vehicles. However, the wide-area deploymentof VFC still confronts several critical challenges such as the lackof efficient incentive and task assignment mechanisms. In thispaper, we address the above challenges and provide a solution tominimize the network delay from a contract-matching integrationperspective. First, we propose an efficient incentive mechanismbased on contract theoretical modeling. The contract is tailoredfor the unique characteristic of each vehicle type to maximizethe expected utility of the base station. Next, we transform thetask assignment problem into a two-sided matching problembetween vehicles and user equipments (UEs). The formulatedproblem is solved by a pricing-based stable matching algorithmwhich iteratively carries out the “propose” and “price-rising”procedures to derive a stable matching based on the dynamicallyupdated preference lists. Finally, numerical results demonstratethat significant performance improvement can be achieved bythe proposed scheme.

Index Terms—vehicular fog computing, resource allocation,task assignment, contract theory, matching theory.

I. INTRODUCTION

W ITH the rapid advancement of information and com-munication technologies, there arises a critical issue

that both the data rate and computation demands grow ex-ponentially. For example, emerging 5G applications such asreal-time video streaming, augmented reality, interactive gam-ing, and self driving, require advanced data communication,computation, and storage techniques to handle the complicateddata processing and storage operations [1]. This poses a newchallenge on the conventional cloud computing paradigm. It

Manuscript received Jan. 11, 2019; revised Jan. 18, 2019.Corresponding author: Junhao Feng (E-mail: junhao [email protected]).Z. Zhou, P. Liu and J. Feng are with the State Key Laboratory of Alternate

Electrical Power System with Renewable Energy Sources, School of Electricaland Electronic Engineering, North China Electric Power University, Beijing,China (E-mal: zhenyu [email protected], pengju [email protected], jun-hao [email protected]).

Y. Zhang is with the Department of Informatics, University of Oslo,Norway. He is also with Simula Research Laboratory, Norway. (E-mail:[email protected])

S. Mumtaz is with the Instituto de Telecomunicacoes, Aveiro, Portugal.(E-mail: [email protected]).

J. Rodriguez is with the Instituto de Telecomunicacoes, Aveiro,Portugal, and University of South Wales, Pontypridd, UK (E-mail:[email protected]).

is difficult to guarantee the stringent quality of service (QoS)and quality of experience (QoE) requirements due to the longdistance between user equipments (UEs) and remote datacenters [2]. Edge computing which extends the computationcapability to the close proximity of UEs has been proposed as acomplementary solution [3], [4]. In [5], Cui et al. investigatedthe energy minimization problem in cache-assisted mobileedge computing (MEC), and proposed a joint caching andoffloading mechanism. Guo et al. proposed an energy-efficientresource allocation scheme for multi-user MEC to optimallyallocate the communication and computation resources [6].However, in order to cover a large-scale geographic area, amassive number of high-cost energy-inefficient servers haveto be deployed and maintained, which inevitably results insignificant capital expenditure (CAPEX) and operational ex-penditure (OPEX). Furthermore, considering the dynamicallytime-varying demands, the dense deployment of servers willlead to huge resource wastage during the off-peak time.Therefore, how to accommodate the ever-increasing demandin communication and computation with moderate costs via ademand-adaptation approach remains an open problem.

An alternative choice is to exploit the under-utilized re-sources of nearby vehicles. Particularly, future vehicles willbe equipped with more powerful onboard computers, larger-capacity data storage units, and more advanced communicationmodules for the sake of improving driving safety, convenience,and satisfaction [7], [8]. Hence, the tremendous computa-tion resources provided by a large group of vehicles canbe aggregated and utilized to alleviate network congestionduring the peak time without deploying additional servers. Forexample, an array of parked vehicles can serve as fog nodeand provide real-time computation capability augmentation[9]. Moreover, the computation tasks of UEs can be directlyoffloaded to vehicles without going through the base stationto further reduce the transmission delay. This new computingparadigm is known as vehicular fog computing (VFC) [10],which is a beneficial complement to edge computing and cloudcomputing.

However, despite the above-mentioned advantages, the widearea deployment of VFC still confronts several critical chal-lenges, which are summarized as follows.

First, there lacks an effective incentive mechanism forvehicles to serve as fog nodes. Most of previous studies haveassumed that vehicles will share their computation resourcesunconditionally [11]. This assumption is too optimistic in




practical implementation. Due to the cost incurred by taskprocessing, self-interested vehicles are reluctant to serve asfog nodes unless they are well compensated. Furthermore, avehicle’s private information, such as the preference towardsresource sharing and the total amount of available resources,is asymmetric, i.e., it is known by the vehicle itself butunavailable for the base station. This is called the scenarioof information asymmetry. Therefore, it is of vital importanceto develop an incentive mechanism, which can effectivelyoptimize the economic benefit of the network operator or thebase station under information asymmetry.

Second, there lacks a low-complexity near-optimal task as-signment mechanism. With the existence of multiple vehiclesand UEs, a critical challenge is how to assign the computationtasks of UEs to vehicles such that the total network delaycan be minimized. Since UEs are owned by independententities, it is highly possible that they have completely differentinterests and even prefer conflicting task assignment decisions.Therefore, a computation task can be implemented if andonly if all the UEs have reached an agreement on the taskassignment decision. Otherwise, some UEs can simply achievea better performance by ignoring the decision. This is differentfrom conventional VFC task assignment problems where theoptimization is performed unilaterally [12], [13].

Accordingly, these challenges motivate us to develop a two-stage computation resource allocation and task assignmentapproach by combining contract theory and matching theory.In the first stage, in order to motivate vehicles to share theirresources, the base station designs a contract, which specifiesthe relationship between the performance, i.e., the amount ofcomputation resources required from a vehicle, and the reward,i.e., the payment to the vehicle for its contribution. In the con-tract, each distinct performance-reward association is definedas a contract item, and a contract generally contains a greatvariety of contract items. Then, the base station broadcasts thecontract, and each vehicle chooses its desired contract item tomaximize its payoff. In the second stage, the vehicles whichhave signed the contract with the base station serve as fognodes. The task assignment problem is modeled as a two-sided matching game, in which the UEs rank the vehicles byconsidering transmission delay, task execution latency, tasksize, and matching cost. A stable matching between UEsand vehicles is derived by using the proposed pricing-basedmatching approach. To the best of the authors’ knowledge,this is the first work which investigates the computationresource allocation and task assignment problem in VFCfrom a contact-matching integration perspective. The maincontributions of this work are summarized as follows:• Contract-based incentive mechanism design: We pro-

pose an efficient incentive mechanism based on contracttheoretical modeling. The contract is tailored for theunique characteristic of each vehicle type to maximize theexpected utility of the base station under the constraintsof individual rationality (IR), incentive compatibility (IC),and monotonicity. To make the problem tractable, thetotal number of IR and IC constraints are firstly reducedby exploring the relationships between adjacent vehicletypes. Then, the simplified problem is solved by using

Karush-Kuhn-Tucker (KKT) conditions. We also considerthe scenario without information asymmetry and derivethe corresponding optimal contract, which is used as aperformance benchmark.

• Matching-based computation task assignment: The taskassignment problem is intractable due to the combina-torial nature. To reduce the complexity, we transformthe task assignment problem into a two-sided matchingproblem based on the problem structure, which involvesa matching between vehicles on one side and UEs onthe other side. Then, we propose a pricing-based stablematching algorithm to solve the task assignment problem,which iteratively carries out the propose and price-risingprocedures to derive a stable matching based on thedynamically updated preference lists.

• Theoretical analysis and performance validation: Weprovide a comprehensive theoretical analysis on con-tract feasibility, matching convergence, matching stabil-ity, matching optimality, and computation complexity.The contract feasibility and efficiency as well as thenetwork delay performance are evaluated by conductinga series of simulations under different scenarios. Nu-merical results demonstrate that the proposed algorithmcan approach the optimal performance of the exhaustivesearching algorithm, while the computation complexity isseveral orders of magnitude lower.

The remaining parts of the paper are summarized as follows.A comprehensive review of related works is provided inSection II. The overall system model is introduced in SectionIII. Section IV presents the contract-based incentive mech-anism design. Section V elaborates the matching-based taskassignment mechanism. Section VI provides the simulationresults. The conclusion is given in Section VII.

II. RELATED WORKS

With the rapid proliferation of vehicles, the studies onVFC have received considerable attentions from both industryand academia. Hou et al. investigated the feasibility of VFCand provided a quantitative analysis among capacity, vehiclemobility, and connectivity [10]. Feng et al. proposed a novelframework named autonomous vehicular edge (AVE) to in-crease the computation capabilities of vehicles in a decentral-ized manner [14]. In [15], Satyanarayanan et al. explored howto build a shared real-time information system for vehiclesto enable situational awareness based on the convergence ofthree technology trends. Xiao et al. investigated the feasibilityof VFC, and developed a cost-effective on-demand VFCarchitecture by leveraging the mobility of vehicles [16]. In[17], Zhu et al. proposed a low-latency quality-enhanced taskassignment solution named fog following me (Folo) for VFC.The task assignment across stationary and mobile fog nodesis formulated as a joint optimization problem, and solvedby exploiting mixed integer linear programming. As we canobserve, these works rely on a common assumption that allthe vehicles are willing to act as fog nodes, and the incentiveissues have been neglected.

There exist some works which have already investigatedthe incentive design problem in cloud/edge/fog computing. In




[18], Luong et al. proposed a comprehensive literature surveyof pricing-based incentive mechanisms for resource allocationin cloud-enabled wireless networks. Liu et al. consideredthe computation offloading problem in MEC, and provideda Stackelberg game-based pricing scheme to stimulate edgeserver owners while optimizing the utility of the cloud serviceoperator [19]. In [20], Su et al. developed a Stackelberggame-based pricing scheme to coordinate the competition andcooperation among moving vehicles, parked vehicles, and roadside unit (RSU). In the Stackelberg game, the leaders, i.e.,the RSU and parking area, have the perfect knowledge ofthe moving vehicles and content delivery costs. In addition,they also know each side’s optimal strategy. However, mostof current works rely on symmetric information, and are notapplicable to the scenario of information asymmetry.

Contract theory is regarded as a powerful tool from microe-conomics to cope with information asymmetry. A vehicle’sprivate information can be effectively elicited because thecontract item is incentive compatible, i.e., the payoff of avehicle is maximized if and only if it selects the contract itemdesigned for its type. Contract theory has already been widelyapplied in the optimization of wireless networks. In [21], Duet al. proposed a contract-based user association approachfor traffic offloading in software-defined heterogeneous net-works. Xu et al. developed an energy-efficient relay selectionscheme by exploiting contract theoretical modeling [22]. Otherapplication scenarios include cognitive radios [23], mobilecrowdsourcing [24], and small-cell caching systems [25].Several previous works have already compared Stackelberggame with contract theory. In [26], Duan et al. investigated theincentive mechanism design for smartphone collaboration. TheStackelberg game is used to model the cooperation game fordata acquisition, where the shared tasks and the correspondingrewards for collaborators are homogeneous. In comparison, thecontract theory is used to motivate cooperation in distributedcomputing, where computation efficiency and task amount forcollaborators heterogeneous. In [24], Liu et al. demonstratedthat the contract theory provides better profit for the basestation than the Stackelberg game due to the fact that thecontract is completely designed by the base station, whichacts as a monopolist in the market. In the Stackelberg game,since the information is symmetric, the followers also knowthe action of the leader, and can optimize their payoffsaccordingly.

Another critical challenge in VFC is how to assign thecomputation tasks to vehicular fog nodes. Numerous studieshave addressed the task assignment problem with differentoptimization approaches, e.g., matching theory [1], [27], coali-tional game [28], Stackelberg game [29], and multi-player non-cooperative game [30]. Compared to other solutions, matchingtheory is more suitable to handle the heterogeneous prefer-ences of UEs. Specifically, the task assignment problem canbe modeled as a two-sided matching game between UEs andvehicles, and solved in a self-organizing and self-optimizingfashion. Matching theory has already been employed to ad-dress various combinatorial problems with mutual preferencesin Internet of things (IoT) fog networks [31], device-to-devicenetworks [12], and vehicular content distribution networks [1],

Fig. 1. The VFC framework.

etc.Based on the above literature review, we can conclude

that there lacks a uniform framework to address the resourceallocation and task assignment optimization problem in VFCfrom a contract-matching integration perspective. Specifically,how to combine these two powerful tools to minimize theoverall network delay requires further investigation.

III. SYSTEM MODEL

The VFC framework is shown in Fig. 1. In each cell,there exists a base station which takes charge of intra-cellcommunication resource coordination, computation resourceallocation and task assignment. During the peak time whenthe base station is overwhelmed by the incoming computationdemands, a group of vehicles are employed to act as fognodes and relieve the overload problem via task offloading.Any vehicle with idle computation resources is able to actas a fog node by sharing its resources for task processing.With a properly-designed incentive mechanism, each vehiclecan actively adjust the amount of resources to be shared inorder to maximize its individual payoff. The details for howto design the incentive mechanism will be illustrated in SectionIV.

In the same cell, there also exist numerous UEs. EachUE generates a series of computation tasks, each of whichcan be either processed by the base station or offloadedto a vehicular fog node. The details for how to model theinteractions between UEs and vehicles, and how to derive alow-complexity sub-optimal task assignment solution will beillustrated in Section V.

For the sake of simplicity, we adopt a time-slot model inwhich the time is slotted into discrete intervals [22]. The opti-




mization process is carried out in a slot-by-slot fashion. The setof vehicles and the set of UEs within the coverage of the basestation remain fixed within each slot, and vary across differentslots, which are denoted as VM = V1, · · · , Vm, · · · , VM andUN = U1, · · · , Un, · · · , UN, respectively. During each slot,it is assumed that each UE, e.g., Un, has a computation task tobe processed. The key attributes of the task can be described bya triplet Dn, Cn, τn, where Dn represents the task data size,Cn is the required computation resource, i.e., the computationsize, and τn represents the delay constraint.

Remark 1. The system model considered in this work canalso be extended to the scenario that a UE has multiplecomputation tasks to be processed per slot. In this case, themultiple tasks can be aggregated and considered as a singletask with larger data size and higher computation demand. IfUE Un has no task, we can simply set Dn = Cn = τn = 0.

Remark 2. Our model is different from the conventionalMEC model where UEs offload their tasks to an edge server.First, the location of the edge server is fixed, while both the fognodes and UEs considered in our model can be mobile. Sec-ond, the incentive issues have been largely neglected in MECsince both the communication and computation infrastructuresare deployed and owned by the same network operator. How-ever, in VFC where vehicles are owned by individuals, theincentive issues must be taken into consideration. Third, inthe MEC model, UEs within the same cell can only connectto one or at most two base stations. In comparison, due tothe high density of vehicles, a UE may be surrounded bymultiple vehicles, and the candidate vehicles of different UEsare overlapped with each other. Last but not least, the MECmodel is more suitable for the centralized task assignmentscenario where the tasks of all the UEs within the same cellare assigned to the same edge server. Our model emphasizeson the decentralized task assignment scenario where the tasksof UEs are assigned to a group of distributed vehicles.

IV. CONTRACT-BASED INCENTIVE MECHANISM DESIGN

In this section, we propose a contract-based incentive mech-anism to motive vehicles to share their computation resourcesfor task offloading. First, we introduce the vehicle type model.Second, the utility functions of the base station and vehiclesare introduced, and the resource allocation problem is formu-lated. Third, we elaborate how to derive the optimal contractunder information asymmetry. Finally, the optimal contractdesign without information asymmetry is provided.

A. Vehicle Type Modeling

The preference of a vehicle towards resource sharing isquantified as its vehicle type. A vehicle with a higher typeis more willing to share its resources and serve as a fog nodecompared to a vehicle with a lower type. Thus, it is intuitivefor the base station to employ higher-type vehicles. Since thenumber of vehicles in a cell is usually finite, the set of vehicletypes belongs to a discrete and finite space. The vehicle typeis defined as follows:

Definition 1. (Vehicle Type): The M vehicles in set VM canbe sorted in an ascending order based on their preferences

and classified into K types. Denote the set of vehicle types asK = 1, · · · , k, · · · ,K, and denote the set of correspondingresource sharing capability as Θ = θ1, · · · , θk, · · · , θK,which is given by

θ1 < · · · < θk < · · · < θK , k ∈ K (1)

Then, we show how to derive the explicit expression of thevehicle type. For vehicle Vm, denote Cm as the computationsize of the local task to be processed. Due to resource sharing,the processing delay will be increased, which is given by

∆τm =Cm

δm,0 − δm− Cmδm,0

≤ ∆τm,max, (2)

where δm,0 and δm represent the total available computationresource and the shared resource, respectively. The inequalityspecifies that the increased delay should be less than or equalto a threshold ∆τm,max to satisfy QoS or QoE requirements.

Through some manipulations of (2), we can derive the upperbound of δm as

δm ≤δ2m,0∆τm,max

δm,0∆τm,max + Cm= δupperm , (3)

where δupperm is the maximum amount of resources that canbe shared. We assume that δupperm falls into a continues closedinterval [δmin, δmax], where δmin and δmax represent the min-imum and maximum values of δupperm ,∀m ∈M, respectively.Then, the interval is divided into K subintervals with the samelength, and the lower bound of the k-th subinterval is definedas θk, which is given by

θk = δmin +k − 1

K(δmax − δmin). (4)

The type of vehicle Vm is said to be k if θk ≤ δupperm < θk+1.Remark 3. From (4), we can infer that θk increases with

δm,0 and ∆τm,max, and decreases with Cm. This definitionis consistent with practical situations. For example, a vehiclewith light local tasks and abundant idle resources can sharemore resources. As a result, it can gain a higher profit andthus has a higher preference towards resource sharing.

In the scenario of information asymmetry, the base stationdoes not know the precise information of each vehicle’stype. Instead, only the statistical knowledge of the vehicletype is available via long term measurements or historicalobservations. We assume that the base station only knowsthat there are a total of K types of vehicles and each vehicleVm ∈ VM belongs to type k with the same probability λk,i.e.,

∑Kk=1 λk = 1.

B. Contract Formulation

Instead of offering the same contract item to vehicleswith different types, the base station can design up to Kcontract items for K vehicle types, i.e., one contract itemper type. For instance, the contract item dedicated for type kvehicle is denoted as (δk, πk), where δk denotes the requiredcomputation resources, and πk is the corresponding reward.The whole contract is denoted as C = (δk, πk),∀k ∈ K.

Assuming the total amount of computation tasks that canbe processed by the base station during a time interval T is




CBS , we have CBS = δBST . Here, δBS is the computationcapability of the base station per second. We assume that thebenefit of the base station is positively related to the reduceddelay, which is valid since the motivation of exploiting VFC isto reduce the computation delay. For the purpose of simplicity,the linear function is utilized, which has also been employed innumerous works [32], [33]. Nevertheless, the proposed schemecan also be extended to more complicated scenarios withnonlinear functions. By signing the contract item (δk, πk) withtype k vehicle, the benefit of the base station is given by

RBS(δk) = rBS(CBSδBS

− CBSδk + δBS

)

= rBSTδk

δBS + δk,

(5)

where rBS is the unit benefit brought by the reduced delay. Itis noted that although (5) is defined as a linear function of thereduced delay, it is actually a concave function of the variableδk, which is nonlinear.

With K types and M vehicles, the expected utility of thebase station is calculated as

UBS(δk, πk) = MK∑k=1

λk[RBS(δk)− πk]. (6)

Remark 4. A contract item (δk = 0, πk = 0) means thattype k vehicle has no desire to share its resources. Moreover,the contract item must also guarantee that the utility of the basestation is nonnegative, i.e., RBS(δk)−πk ≥ 0. Otherwise, thebase station has no incentive to sign the contract with type kvehicle.

The utility function of type k vehicle which accepts thecontract item (δk, πk) is given by

UVk (δk, πk) = θkπk − δk, (7)

where θk characterize the weight of πk to type k vehicle.A higher-type vehicle has a larger weight due to its higherpreference towards resource sharing.

The expected social welfare is the total sum utility of thebase station and the M vehicles, which is given by

Us(δk, πk) = UBS(δk, πk) +MK∑k=1

λkUVk (δk, πk).

(8)

The objective of the base station is to maximize its utilityunder the scenario of asymmetric information via the optimiza-tion of each contract item. The corresponding optimizationproblem is formulated as

P1 : max(δk,πk)

UBS(δk, πk)

s.t. C1 : θkπk − δk ≥ 0,∀k ∈ K, (IR)

C2 : θkπk − δk > θkπk′ − δk′ ,∀k, k′ ∈ K, k 6= k′, (IC)

C3 : 0 ≤ δ1 < · · · < δk < · · · < δK ,∀k ∈ K,C4 : δk ≤ θk,∀k ∈ K, (9)

where C1, C2, and C3 represent the IR, IC, and monotonicityconstraints, respectively. C4 represents the upper bound of δk.

Definition 2. The IR, IC, and monotonicity constraints aredefined as follows:• Individual rationality (IR) constraint: Type k vehicle,∀k ∈ K, will get a nonnegative payoff if it selects thecontract item (δk, πk).

• Incentive compatibility (IC) constraint: The IC con-straint ensures the self-revealing property of the contract.For instance, type k vehicle, ∀k ∈ K, will get themaximum payoff if and only if it selects the contract item(δk, πk) designed for its own type.

• Monotonicity constraint: The reward of type k vehicle,∀k ∈ K, should be higher than that of type k−1 vehicle,and lower than that of type k + 1 vehicle.

Based on the IR, IC, and monotonicity constraints, we have

Lemma 1. For any k, k′ ∈ K, if θk > θk′ , then δk > δk′ andπk > πk′ . πk = πk′ and δk = δk′ if and only if θk = θk′ .

Lemma 2. For any (δk, πk) ∈ C, the following inequalitieshold

0 ≤ π1 ≤ · · · ≤ πk ≤ · · · ≤ πK ,0 ≤ δ1 ≤ · · · ≤ δk ≤ · · · ≤ δK ,0 ≤ UV1 ≤ · · · ≤ UVk ≤ · · · ≤ UVK . (10)

Proof: A similar proof of Lemma 1 and Lemma 2 canbe found in [34]. The details are omitted here due to spacelimitation.

Based on Lemma 1 and Lemma 2, we define the sufficientand necessary conditions for contract feasibility.

Theorem 1. Contract feasibility: The contract C =(δk, πk), ∀k ∈ K is feasible if and only if all the followingconditions are satisfied:• 0 ≤ π1 ≤ · · · ≤ πk ≤ · · · ≤ πK and 0 ≤ δ1 ≤ · · · ≤δk ≤ · · · ≤ δK;

• θ1π1 − δ1 ≥ 0;• For any k ∈ 2, · · · ,K, δk−1 + θk−1(πk − πk−1) ≤δk ≤ δk−1 + θk(πk − πk−1).

Proof: The detailed proof of Theorem 1 is omitted heredue to space limitation. A similar proof can be found inAppendix D of [23].

C. Optimal Contract Design under Information Asymmetry

Problem P1 involves K IR constraints and K(K − 1)IC constraints. To provide a tractable solution, the followingprocedures are carried out to simplify the problem.

Step 1: IR Constraints EliminationFor type k vehicle, k ∈ K, k 6= 1, we can derive

UVk ≥ UVk−1 ≥ UV1 ≥ 0, (11)

where the first inequality is due to the IC constraint, the secondinequality is based on Lemma 2, and the third inequality isdue to the IR constraint. Hence, the IR constraint of type kvehicle holds automatically as long as the IR constraint of type1 vehicle is guaranteed.

Step 2: IC Constraints Elimination




We define the IC constraints between type k and typek′, k′ ∈ 1, · · · , k − 1, as downward incentive constraints(DICs). Similarly, the IC constraints between type k and typek′′, k′′ ∈ k + 1, · · · ,K, are defined as upward incentiveconstraints (UICs). In the following, we show that both theDICs and UICs can be reduced.

We consider three adjacent vehicle types, i.e., θk−1 < θk <θk+1, which satisfy

θk+1πk+1 − δk+1 ≥ θk+1πk − δk, (12)θkπk − δk ≥ θkπk−1 − δk−1, (13)

where (12) denotes the DIC between type k + 1 and k, and(13) denotes the DIC between type k and k − 1.

By combining πk+1 ≥ πk ≥ πk−1, we have

θk+1πk+1 − δk+1 ≥ θk+1πk−1 − δk−1. (14)

Therefore, if the DIC between type k + 1 and k holds, thenthe DIC between type k + 1 and k − 1 also holds. The DICconstraints can be extended downward from type k−1 to type1, which are given by

θk+1πk+1 − δk+1 ≥ θk+1πk−1 − δk−1≥ · · ·≥ θk+1π1 − δ1.

(15)

Thus, we demonstrate that if the DICs between adjacenttypes hold, then all the DICs hold automatically. Similarly,we can demonstrate that if the UICs between adjacent typeshold, then all the UICs hold automatically.

Based on the above analysis, the K IR constraints andK(K − 1) IC constraints can be reduced to 1 and K − 1,respectively. Furthermore, we have the following properties:

Proposition 1. In order to maximize the utility of the basestation, the optimal contract item for type 1 vehicle, i.e.,(δ∗1 , π

∗1), must enforce

UV1 (δ∗1 , π∗1) = θ1π

∗1 − δ∗1 = 0. (16)

Proof: The proof is based on reduction to absurdity.Assuming θ1π

∗1 − δ∗1 > 0, then the base station can improve

its own utility by either decreasing π∗1 or increasing δ∗1 untilθ1π1 − δ1 = 0 while simultaneously satisfying the conditionsof contract feasibility. Then, we have

RBS(δ1)− π1 > RBS(δ∗1)− π∗1 , (17)

which contradicts with the assumption that (δ∗1 , π∗1) is the

optimal contract item. Hence, we must have θ1π∗1 − δ∗1 = 0.This completes the proof of Proposition 1.

Proposition 2. The optimal contract item for any type kvehicle (δ∗k, π

∗k), k = 2, · · · ,K, satisfies the following equality

condition:

δ∗k = δ∗k−1 + θk(π∗k − π∗k−1). (18)

Proof: From the IC constraint, we have

δ∗k ≤ δ∗k−1 + θk(π∗k − π∗k−1), k = 2, · · · ,K (19)

Then, the base station can further improve its own utility byeither decreasing π∗k or increasing δ∗k until the equality holds,

which does not violate the conditions of contract feasibility.This completes the proof of Proposition 2.

Thus, based on constraint elimination, Proposition 1 andProposition 2, P1 can be rewritten as

P2 : max(δk,πk)

UBS(δk, πk),

s.t. C1 : θ1π1 − δ1 = 0, (IR)

C2 : δk = δk−1 + θk(πk − πk−1), 2 ≤ k ≤ K, (IC)

C3, C4,∀k ∈ K. (20)

We can easily prove that P2 is a convex programming prob-lem by checking the Hessian matrix. Thus, P2 can be solvedby applying KKT conditions. The Lagrangian associated withP2 is given by

L(δk, πk, µk, ρk, βk)= UBS(δk, πk) + µ1(θ1π1 − δ1)

+K∑k=2

µk

(θk(πk − πk−1) + δk−1 − δk

)+ ρ1δ1 +

K∑k=2

ρk(δk − δk−1) +K∑k=1

βk(δk − θk),

(21)

where µ1 is the Lagrange multiplier corresponding to con-straint C1, µk, k = 2, · · · ,K, ρk,∀k ∈ K, and βk,∀k ∈K are the vectors of Lagrange multipliers corresponding toconstraints C2, C3, and C4, respectively. KKT conditions aresummarized as follows:• Primal constraints: 0 ≤ δ∗1 ; δ∗k−1 ≤ δ∗k, δ

∗k = δ∗k−1 +

θk(π∗k−π∗k−1),∀k ∈ K, k 6= 1; δ∗1 = θ1π∗1 ; δ∗k ≤ θk,∀k ∈

K;• Dual constraints: µ∗k ≥ 0, ρ∗k ≥ 0 and β∗k ≥ 0,∀k ∈ K;• Complementary slackness: ρ∗1δ

∗1 = 0; ρ∗k(δ∗k − δ∗k−1) =

0,∀k ∈ K, k 6= 1; β∗k(δ∗k − θk) = 0,∀k ∈ K ;• The first-order conditions of the Lagrangian is

∂L∂δk

=∂RBS(δk)

∂δk− µk + µk+1 + ρk − ρk+1

+ βk = 0,∀k ∈ K, k 6= K,

∂L∂δK

=∂RBS(δK)

∂δK− µK + ρK + βK = 0,

∂L∂πk

=− λk + µkθk − µk+1θk+1 = 0,

∀k ∈ K, k 6= K,

∂L∂πK

=− λK + µKθK = 0.

(22)

The contract design and optimization is handled by the cen-tralized base station, and the detailed process is summarizedas part of the Algorithm 1.

D. Optimal Contract Design without Information Asymmetry

If there exists a selfish base station which is perfectlyaware of every vehicle’s type, it can further increase itsprofit by exploiting the complete information. The contracthas to ensure that the payoff of each vehicle is non-negative.Otherwise, the vehicles have no incentive to accept the contract




items. To this end, the contract item also has to meet the IRconstraint. Furthermore, the contract item has to satisfy thefollowing property:

Theorem 2. In the contract design without information asym-metry, any optimal contract item (δ∗k, π

∗k) ∈ C should satisfy

θkπ∗k = δ∗k. That is, the payoff for any vehicle is zero.

Proof: Theorem 2 can be proved by contradiction. Givenan optimal contract item (δ∗k, π

∗k), if θkπ∗k − δ∗k > 0, then

the base station can increase its utility by decreasing π∗k toπk which satisfies θkπk − δ∗k = 0. This contradicts with theassumption that (δ∗k, π

∗k) is optimal.

Thus, by enforcing the utility of each vehicle to be zero,P2 can be written as

P3 : max(δk,πk)

UBS(δk, πk),

s.t. C1 : θkπk − δk = 0,∀k ∈ K,C3, C4. (23)

P3 can also be solved by using KKT conditions.

Theorem 3. In the contract design without information asym-metry, for any type k vehicle, k ∈ K, the optimal reward isπ∗k = 1 regardless of θk.

Proof: From Theorem 2, we have θkπ∗k − δ∗k = 0.

Furthermore, from the upper bound of δk ≤ θk, we can deriveδ∗k = θk since the base station can always increase δk toincrease its utility until the equality holds. Thus, we haveθkπ∗k − θk = 0, and π∗k = 1.

V. MATCHING-BASED TASK ASSIGNMENT

In this section, we first introduce the task assignmentmodel and the problem formulation. Then, we introduce theproposed pricing-based matching algorithm. Next, we providea comprehensive theoretical analysis on convergence, stability,optimality, and complexity.

A. Task Assignment Model

1) Task Transmission Delay: After the first-stage resourcesharing, the UEs can offload their computation tasks to vehi-cles which serve as fog nodes. In the offloading mode, datacan be directly transmitted from UEs to vehicles to reduce thetotal number of transmission hops. We assume that each UEis allocated with an orthogonal spectrum resource block suchthat the co-channel interference among UEs can be ignored.Furthermore, the large-scale fading and the small-scale fadingare modeled by using the Rayleigh fading model and the free-space propagation path-loss model, respectively. If the task ofUE Un is offloaded to vehicle Vm, the signal to noise ratio(SNR) of the received signal at vehicle Vm is given by

γm,n =pnd−αn,mh

2n,m

N0, (24)

where pn denotes the transmission power of UE Un. dn,m isthe transmission distance between UE Un and vehicle Vm. α isthe path-loss exponent. hn,m represents the Rayleigh channel

coefficient with a complex Gaussian distribution. N0 denotesthe power noise.

Hence, the transmission time required by UE Un for up-loading its task with size Dn can be obtained as

T tn,m =Dn

Bn,m log2 (1 + γn,m), (25)

where Bn,m refers to the bandwidth of the link between UEUn and vehicle Vm.

We assume that the vehicles travel on a two-lane two-directional road. Due to the fast vehicle mobility, vehicleVm might move out of the communication range of UE Unduring data transmission, which results in an offloading failure.Denote the dwell time of Vm inside the communication rangeof Un as τon,m. An offloading failure occurs if τon,m < T tn,m.Therefore, τon,m also represents the delay constraint of datatransmission because Un can only transmit data to Vm whenthey remain connected. That is, an offloading request isadmissible if and only if T tn,m < τon,m.

To estimate the vehicle dwell time, a simple way is to usethe average velocity. Assuming that UE Un is located alongthe road side and its communication range is a circle with adiameter dn, τon,m can be calculated as

τon,m = dn,m/vm, (26)

where dn,m denotes the distance between the location of Vmand the endpoint of the circle’s diameter in the vehicle headingdirection, and vm denotes the average velocity of Vm.

Remark 5. Both dn,m and vm can be estimated from theGPS data [35]. For example, if Vm moves in the centrifugaldirection to leave the communication area of Vn, dn,m iscalculated as dn,m = 1

2dn− dn,m. Otherwise, if Vm moves in

the centripetal direction, we have dn,m = 12dn

+dn,m. We havenot put any restriction on the mobility models of vehicles. Aslong as the vehicle dwell time can be obtained, the proposedmatching-based task assignment scheme can be adaptable fordifferent mobility models.

Remark 6. In this work, we assume that the GPS infor-mation is known to the base station. This assumption hasalso been accepted and employed in a number of previousworks [8], [14]. Furthermore, even if the GPS information isunavailable to the base station, vehicle positions can still beobtained based on mobility prediction techniques [36]–[39].

2) Task Execution Delay: If the type of vehicle Vm is k, i.e.,the amount of computation resource is δm = δ∗k, the executiontime required to process the task of UE Un is calculated as

T cn,m =Cnδm

=Cnδ∗k. (27)

The transmission latency from Vm to Un is ignored, due tothe fact that the size of computation results is usually negligi-ble compared to that of the input data, e.g., face recognition.If Vm has already moved out of the communication range ofUn, the results have to be forwarded firstly from Vm to thebase station, and then sent from the base station to Un.

The total delay when the task of UE Un is assigned tovehicle Vm is given by

T totaln,m = T tn,m + T cn,m. (28)




3) Problem Formulation: The purpose of this work is torelieve the heavy burden of the base station and reduce the totalnetwork delay by leveraging the under-utilized computationresources of vehicles. Hence, we model the objective functionas the total delay of the overall network, i.e., the sum delayof all the UEs. We investigate how to assign the tasks of UEsto vehicles such that the objective function is minimized. Thetask assignment decision is defined as follows:

Definition 3. (Task Assignment Decision): The task assign-ment decision between N UEs and M vehicles is definedas a N × M matrix X, where its (n,m)-th element , i.e.,xn,m, is defined as a binary value. xn,m = 1 means thatthe computation task of UE Un is assigned to vehicle Vm.Otherwise, xn,m = 0.

The problem is formulated as follows:

P4 : minX

N∑n=1

M∑m=1

xn,mTtotaln,m

s.t. C5 :∑

Vm∈VM

xn,m ≤ 1,∀Un ∈ UN ,

C6 :∑

Un∈UN

xn,m ≤ 1, ∀Vm ∈ VM ,

C7 : T totaln,m ≤ τn,∀Un ∈ UN ,∀Vm ∈ VM ,C8 : T tn,m ≤ τon,m,∀Un ∈ UN ,∀Vm ∈ VM . (29)

Here, C5 and C6 guarantee that there is a one-to-one corre-spondence among UEs and vehicles. C7 and C8 denote thedelay constraints of task assignment and task transmission,respectively.

To provide a tractable solution, the combinatorial problemP4 can be transformed into a two-sided matching problembased on the problem structure. The matching problem can berepresented as a triple (UN ,VM ,F), where UN and VM aretwo distinct and finite sets of matching participants, i.e., UEsand vehicles, respectively. F represents the set of matchingpreferences of UEs. Particularly, each UE aims at minimizingits individual delay under the specified constraints. A one-to-one matching φ is defined as [40]:

Definition 4. (Matching): For the formulated matching prob-lem (UN ,VM ,F), the matching φ is a one-to-one correspon-dence from set UN ∪MK onto itself under preference F , i.e.,φ(Un) ∈ VM ∪ Un, ∀Un ∈ UN . φ(Un) = Vm representsthat UE Un is matched with vehicle Vm, which is equivalent toxn,m = 1. φ(Un) = Un means that Un has not been matchedwith any vehicle, and the task of Un will be handled by thebase station.

B. Preference List Construction

In order to implement the two-sided matching, every UEhas to construct its preference list by ranking vehicles fromthe other side in accordance with the preferences. For UEUn, it can achieve different delay performances when beingpaired with different vehicles. Therefore, in order to minimizethe total delay, we can define that the preference is inversely

proportional to the total delay, e.g., 1/T totaln,m . The preferenceof Un towards Vm is calculated as

Gn,m∣∣φ(Un)=Vm

=1

T totaln,m

− Pm, (30)

where Pm is the price for utilizing the computation resourceof Vm, the initial value of which is zero. The role of Pm is toresolve the matching conflict, which will be explained later.Here, 1/T total is just used as an example. The preferencemodel can be extended to more complicated expressions.

We introduce a complete, reflexive, and transitive binarypreference relation [40], i.e., “”, to compare the preferencestowards different vehicles. For instance, Vm Un Vm′ repre-sents that Un prefers Vm to Vm′ , which is given by

Vm UnVm′ ⇔ Gn,m|φ(Un)=Vm

> Gn,m′ |φ(Un)=Vm′ . (31)

Furthermore, Vm UnV

′

m represents that Un prefers Vm atleast as well as V

′

m, which is given by

Vm UnVm′ ⇔ Gn,m|φ(Un)=Vm

≥ Gn,m′ |φ(Un)=Vm′ . (32)

To obtain the entire preference list of Un, we temporarilypair it with every vehicle in order to derive the preferencefor each combination. We use Fn to denote the preferencelist of Un towards all the vehicles. Fn is obtained by sort-ing all the M vehicles in a descending order according toGn,m|φ(Un)=Vm

,∀Vm ∈ VM . The total set F is constructedas F = Fn,∀Un ∈ UN.

C. Pricing-based Stable Matching

After obtaining the preference for all the UEs in UN , thesecond-stage task assignment problem can be solved by usinga pricing-based stable matching algorithm. The main parts ofit are the propose and the price rising rules, which are definedas follows:

Definition 5. (Propose Rule): For any UE Un ∈ UN ,it proposes to its most preferred vehicle which ranks asthe first place in its preference list Fn, e.g., Vm. We haveVm Un

Vm′ ,∀Vm′ ∈ Fn, Vm′ 6= Vm.

Definition 6. (Price Rising Rule): For any vehicle Vm ∈ VMthat has received more than one proposal from UEs, it canraise its price to increase the matching cost, which is givenby

Pm = Pm + ∆Pm. (33)

The matching process is implemented in an iterative fashion,and the detailed process is summarized as part of the Algo-rithm 1. It is noted that the matching-based task assignmentcan also be managed by the base station. Specifically, eachUE uploads its preference list to the base station, and then astable matching between UEs and vehicles is derived by thebase station based on the preference lists of UEs. Eventually,the base station broadcasts the matching result to UEs, whichoffload their tasks to the corresponding vehicles accordingly.The implementation procedure is explained as follows.

Phase 1: Matching Preference Initialization• Calculate Fn for each UE Un ∈ UN .




• Initialize φ as an empty set. Define Ω as the set ofvehicles which receive more than one matching proposal.Ω = ∅ at the beginning.

• Set Pm = 0 for any vehicle Vm ∈ VM .Phase 2: Iterative MatchingRepeat the following process iteratively.• If ∃φ(Un) = ∅, preform the propose rule for UEs.

– Each UE Un ∈ UN proposes to its most preferredvehicle in its preference list Fn.

• If any vehicle Vm ∈ VM receives only one proposal froma UE, then Vm will be directly matched with the UEwhich has proposed to it. Otherwise, add Vm into set Ω.

• If Ω 6= ∅, perform the price rising rule for vehicles whichreceived more than one matching proposal.

– Each vehicle Vm ∈ Ω increases its price by ∆Pm.– Every UE which has proposed to Vm updates its

preference towards Vm accordingly and renews itsproposal.

– Remove the vehicles which receive only one pro-posal from Ω.

Until Every Un has been matched with a vehicle, i.e.,∀φ(Un) 6= ∅, or there exists no available vehicle for theunmatched UEs.

Phase 3: Task Assignment ImplementationThe UEs offload their tasks according to the matching

results obtained in Phase 2. Assuming φ(Un) = Vm, UEUn will send its task to vehicle Vm for processing. For thoseunmatched UEs in set Φ, their tasks will be processed by thebase station. In the next slot, the base station updates the setsUN and VM , and the task assignment process will return toPhase 1.

Remark 7. It is noted that any vehicle Vm ∈ VM , whichcannot satisfy the delay constraint of Un, will be directlyremoved from Fn despite of the preference.

D. Stability, Optimality and Complexity Analysis

Definition 7. (Stability): A matching φ is stable if for anyUn ∈ UN , there does not exit a Vm such that Vm Un

φ(Un).

Theorem 4. The pricing-based matching algorithm producesa stable matching within finite iterations.

Theorem 5. The obtained stable matching is weak Paretooptimal for UEs.

Proof: A similar proof can be found in our previous works[1], [12].

Remark 8. (Computational Complexity) In the contract-based incentive mechanism design, the formulated optimiza-tion problem is a standard convex programming problem withM equality constraints and 2M+1 inequality constraints. Theoverall computation complexity is O(M).

In the process of the pricing-based matching, the complexityfor each UE to acquire the preferences of all the vehiclesand the complexity for sorting the obtained preferences areO(M) and O(M log(M)), respectively. Assuming the numberof iterations required for resolving the conflict in the pricerising process is ζ, i.e., the conflicting elements are matched

Algorithm 1 Contract-Matching Algorithm1: Input: M , N , θk, λk2: Output: C∗, φ

Stage I: Contract-based Incentive Mechanism Design3: Sort the types of vehicles based on (4);4: Obtain the optimal contract C∗ by solving (20);5: for Vm ∈ VM do6: Calculate the maximum amount of shared resource

δupperm based on (3).7: if θk ≤ δupperm < θk+1 then8: Vm signs the contract item (δ∗k, π

∗k) with the base

station, and shares its idle resource δ∗k.9: end if

10: end forStage II: Matching-based Task Assignment

11: Set φ=∅, Ω=∅, ∆Pm=0.1, Pm=0 and Uvm = ∅ for eachVm ∈ VM ;

12: Every UE Un ∈ UM builds its preference list Fn basedon (30) and (31);

13: while ∃φ(Un) = ∅ do14: for Un ∈ UN do15: UE Un proposes to its most preferred vehicle in its

updated preference list Fn;16: end for17: for Vm ∈ VM do18: if Vm receives more than one request then19: Ω = Ω ∪ Vm;20: Add UEs which proposed to vehicle Vm to the set

Uvm ;21: end if22: end for23: if Ω = ∅ then24: Match vehicles with UEs based on the proposals;25: else26: for Vm ∈ Ω do27: Vehicle Vm increases its price Pm by ∆Pm based

on (33);28: Every Un ∈ Uvm updates its preference based on

(30), and renews its proposals;29: Remove Un from Uvm if it gives up Vm;30: Remove Vm from Ω if it receives only one pro-

posal.31: end for32: end if33: end while

within ζ iterations. Hence, the complexity of the matchingprocess is O(Nζ)(N ≥M) or O(Mζ)(M ≥ N).

The optimal matching result can be obtained by employingthe exhaustive searching scheme. The total number of possiblecombinations is (MNN !). Thus, the exhaustive searchingscheme has to examine every possible combination in orderto find out the optimal matching result. The computationcomplexity is O(MNN !).




0 2 4 6 8 10 12 14 16 18 20

Type of Contract Items

0

100

200

300

400

500

600

700

800

Sh

are

d C

om

pu

tatio

n R

eso

urc

es

Information Asymmetry

No Information Asymmetry

(a) The shared computation resources versus dif-ferent types of vehicles.

0 2 4 6 8 10 12 14 16 18 20

Type of Contract Itemss

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Re

wa

rds



(b) The rewards versus different types of vehicles.

0 2 4 6 8 10 12 14 16 18 20


-100

-50

0

50

100

150

200

250

Utilit

y o

f V

eh

icle

s

Type-5

Type-10

Type-15

(c) The utility of vehicles versus different types ofcontract items.

Fig. 2. Contract feasibility: (a) shared computation resources; (b) rewards; (c) utility of vehicles.

0 2 4 6 8 10 12 14 16 18 20


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Utilit

y o

f th

e B

ase S

tation



Take-it-or-leave Contract

(a) The utility of the base station versus differenttypes of vehicles.

0 2 4 6 8 10 12 14 16 18 20


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Utilit

y o

f V

ehic

les




(b) The utilities of vehicles versus different typesof vehicles.

0 2 4 6 8 10 12 14 16 18 20


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Socia

l W

elfare




(c) The social welfare versus different types ofvehicles.

Fig. 3. Contract efficiency: (a) utility of the base station; (b) utilities of vehicles; (c) social welfare.

TABLE IPARAMETERS.

Parameter ValueNumber of vehicles 5− 20Number of UEs 6− 25Data size of UE’s task 100− 200 MbComputation size of UE’s task 100− 400 MbDelay constraint 0.1− 2 sVelocity of vehicles 2− 20 m/sCell radius 1000 mRadius of the UE’s communication coverage 200 mComputing resources of the base station 5 GHzTransmission power of UEs 30 dBmBandwidth of UEs 20 MHzNoise power −114 dBmPath loss exponent −3.4

VI. SIMULATION RESULTS

In this section, we validate the proposed scheme via simu-lations.

A. Contract Feasibility and Efficiency

A series of simulations are conducted to verify the fea-sibility and the efficiency of the contract-based incentive

mechanism. We consider a single cell with one base station, 20vehicles, and 30 UEs. The number of vehicle types is equal tothat of vehicles, and assume the vehicle types are following aGaussian distribution. Simulation parameters are summarizedin Table I. The proposed scheme is compared with the contractwithout information asymmetry [34] and the take-it-or-leavecontract [23]. In the take-it-or-leave contract, the base stationoffers a uniform contract item which is designed based ona threshold type kth. Then, vehicles with higher types, i.e.,k ≥ kth,∀k ∈ K, will accept the contract, while vehicles withlower types, i.e., k < kth,∀k ∈ K, will reject the contract.

Fig. 2(a) and Fig. 2(b) show the amount of shared com-putation resources and the rewards versus different vehicletypes, respectively. As we can see, the computation resourcesthat can be shared by vehicles and the corresponding rewardincrease monotonically with the vehicle type, which have beenalready demonstrated in Lemma 2. Furthermore, numericalresults show that the contract without information asymmetryrequires more resources from vehicles compared to that ofinformation asymmetry. The reward provided for each vehicleis exactly 1 regardless of the vehicle type, which is consistentwith Theorem 3.

Fig. 2(c) shows the utilities of type 5, type 10, and type15 vehicles versus the different types of contract items. It




0 1 2 3 4 5 6 7 8

Number of Matching Iterations

0.7

0.75

0.8

0.85

0.9

0.95

1

No

rma

lize

d N

etw

ork

De

lay

N=15

N=20

N=25

Fig. 4. Normalized delay of UEs vary with the number of iterations.

6 8 10 12 14 16 18 20 22

Number of UEs

0.5

No

rma

lize

d N

etw

ork

De

lay

Optimal Matching

Optimal Matching

Stable Matching

Stable Matching

0

2

Co

mp

uta

tio

n C

om

ple

xity

×1036

Fig. 5. Normalized delay and computation complexity versus the number ofUEs.

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Delay Constraint

0.75

0.8

0.85

0.9

0.95

1

No

rma

lize

d N

etw

ork

De

lay

Stable Matching, M=3

Optimal Matching, M=3



Fig. 6. Normalized delay versus the delay constraint τn.

2 4 6 8 10 12 14 16 18 20

Velocity of Vehicles

0.75

0.8

0.85

0.9

0.95

1

No

rma

lize

d N

etw

ork

De

lay





Fig. 7. Normalized delay versus the velocity of vehicles.

is observed that each vehicle can maximize its utility if andonly if it selects the specific contract item dedicated for itstype. Furthermore, numerical results show that the utilities ofvehicles also increase with the vehicle type, which agrees withthe analysis summarized in Lemma 2.

Fig. 3(a) and Fig. 3(b) show the utility of the base stationand the utility of vehicles versus the vehicle type. Numericalresults show that the asymmetric information actually protectsthe vehicles from being overexploited by the base station.With complete information, the base station is able to designa contract such that its utility is much larger compared tothe utility achieved under the information asymmetry scenario.The performance gap increases monotonically with the vehicletype. Moreover, the contract enforces every vehicle’s utilityto be zero. The reason behind has been analyzed in theproof of Theorem 2. Therefore, information asymmetry isactually beneficial to the vehicles because the base stationcannot overexploit a vehicle without knowing the completeinformation of its type.

In the take-it-or-leave contract, any vehicle whose type

satisfies k < kth,∀k ∈ K will reject the contract due toconstraint C4. In this case, either the base station’s utilityor the vehicle’s utility is zero. Only the vehicles with highertypes, i.e., k ≥ kth,∀k ∈ K, can achieve nonzero utilities.However, since the take-it-or-leave contract is designed basedon threshold type kth, the gap between the utility of typek vehicle and that of the proposed scheme increases alongwith k. The reason is that the take-it-or-leave contract is notincentive compatible.

Fig. 3(c) shows the social welfare versus the vehicle type.Numerical results demonstrate that the social welfare achievedby the proposed contract is close to that of the contract withoutinformation asymmetry. The reason is that the utility of thebase station obtained by exploiting the complete informationleads to enormous utility loss of vehicles. On the other hand,the take-it-or-leave contract achieves the lowest social welfare.

B. Delay Performance

In simulations, we employ the constant-velocity model [10],[20], and the velocities of vehicles are generated randomly




within the range [2, 20] m/s. To provide a relative comparison,the delay performances of different algorithms are normalizedand converged to the range of [0, 1] by dividing the largestdelay.

Fig. 4 shows the normalized network delay versus thenumber of matching iterations. Numerical results show that theproposed scheme can converge to a stable matching within alimited number of iterations. It is also observed that both thenumber of iterations required to reach convergence and thenormalized network delay increase with the number of UEs.The reason is that the competition among UEs becomes moreintense as the number of UEs increases. As a result, additionalprice-rising iterations are necessary to resolve the competition.Moreover, if the number of UEs is much larger than that ofvehicles, a larger amount of tasks have to be processed bythe overloaded base station, which significantly increases thenetwork delay.

Fig. 5 shows the normalized network delay versus thenumber of UEs. Numerical results demonstrate that the net-work delay is inversely related to the number of vehicles andpositively related to the number of UEs, which is consistentwith the results of Fig. 4. Furthermore, the proposed schemeis able to achieve a network delay that is close to that of theoptimal exhaustive searching algorithm but with a much lowercomplexity.

Fig. 6 shows the normalized network delay versus thetotal delay constraint of the computation task. As the totaldelay constraint increases, the number of eligible vehiclesalso increases accordingly, and more and more tasks can beoffloaded to the vehicles rather than being processed by theoverloaded base station with limited computation resources.This will dramatically reduce the network delay since theunder-utilized resources of vehicles have been well exploited.Numerical results also demonstrate that the proposed schemecan achieve close-to-optimal performance under all the inves-tigated scenarios.

Fig. 7 shows the normalized network delay versus the ve-hicle velocity. Numerical results demonstrate that the networkdelay increases with the vehicle velocity. The reason is that thenumber of eligible vehicles decreases along with the vehiclevelocity due to the stringent constraint of transmission delay.As a result, it is less likely for a UE to be matched with asatisfactory vehicle, and the corresponding task can only beprocessed by the overloaded base station. Hence, the proposedscheme is more suitable for hot spots where there exist a largenumber of parked vehicles or the vehicles move slowly dueto traffic congestion.

VII. CONCLUSION

In this paper, we investigated the computation resource allo-cation and task assignment problem in VFC from a contract-matching integration perspective. A contract-based incentivemechanism was proposed to motivate vehicles to share theirresources, and a pricing-based stable matching algorithm wasdeveloped to address the task assignment problem. Numericalresults demonstrate that the proposed incentive mechanismachieves a social welfare that is close to the optimal per-formance without information asymmetry, while the proposed

task assignment scheme is able to achieve a network delay thatis close to that of the optimal exhaustive searching algorithmbut with a much lower complexity.

In future works, we will investigate the more complicatedscenario where the precise knowledge of channel and vehi-cle states is unknown, and study how to combine machinelearning-based approaches to optimize the long-term delayperformance.

Furthermore, the wide-scale deployment of VFC faces nu-merous security and forensic challenges. Different from cloudcomputing where the servers are deployed, operated, andmaintained by specialized service providers, the fog nodes aregenerally deployed and maintained by third-party developersor even users. Therefore, to guarantee the reliable operationof VFC, several security mechanisms including confidentiality,integrity, authentication, access control, and forensics, etc.,are required [41]. However, some existing security solutionsdeveloped for cloud computing may not scale well in VFC[42]. Particularly, the heterogeneous and distributed nature offog nodes poses new threats on authentication, access control,and resilience [42]. In summary, the research on the securityaspect of VFC is still in the infancy stage, which requiresfurther investigation and examination.

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Zhenyu Zhou (S06-M11-SM17) received the M.E.and Ph.D. degrees from Waseda University, Tokyo,Japan, in 2008 and 2011, respectively. From April2012 to March 2013, he was the Chief Researcherwith the Department of Technology, KDDI. Since2013, he has been an Associate Professor withthe School of Electrical and Electronic Engineer-ing, North China Electric Power University, Bei-jing, China. He has also been a Visiting Scholarwith Tsinghua-Hitachi Joint Lab on Environment-Harmonious ICT, Tsinghua University, since 2014.

His research interests include green communications and smart grids.Dr. Zhou served as an Associate Editor for IEEE Access, a Guest Editor

for IEEE Communications Magazine, workshop co-Chair for the 2015 IEEEInternational Symposium on Autonomous Decentralized Systems, and a TPCmember for IEEE VTC, IEEE ICC, IEEE Globecom, IEEE PIRMC, IEEEAPCC, IEEE Africon, IEEE CCNC, etc. He received 2017 Premium Awardfor Best Paper in IET Communications, Young Researcher EncouragementAward from the IEEE Vehicular Technology Society in 2009 and BeijingOutstanding Young Talent from Beijing Government, China.

Pengju Liu is currently working towards the Bache-lor degree at North China Electric Power University,China. His research interests include resource allo-cation, energy management in VEC.

Junhao Feng is currently working towards the M.S.degree at North China Electric Power University,China. His research interests include resource allo-cation, interference management, and energy man-agement in D2D communications.




Yan Zhang (M’05-SM’10) received the Ph.D. de-gree from the School of Electrical and Electron-ics Engineering, Nanyang Technological University,Singapore. He is currently a Full Professor withthe Department of Informatics, University of Oslo,Oslo, Norway. His current research interests includenext-generation wireless networks leading to 5G,green and secure cyber-physical systems, such assmart grid, healthcare, and transport. He is an IEEEVehicular Technology Society (VTS) DistinguishedLecturer. He is also a Senior Member of the IEEE

ComSoc, the IEEE CS, the IEEE PES, and the IEEE VTS. He is a fellow ofthe IET. He is an Associate Technical Editor of the IEEE CommunicationsMagazine, an Editor of IEEE Network Magazine, an Editor of the IEEETransactions on Green Communications and Networking, an Editor of theIEEE Communications Surveys and Tutorials, an Editor of IEEE Internet ofThings Journal, and an Associate Editor of the IEEE Access. He serves as theChair in a number of conferences, including the IEEE GLOBECOM 2017,the IEEE PIMRC 2016, the IEEE CloudCom 2016, the IEEE ICCC 2016,the IEEE CCNC 2016, the WCSP 2016, the IEEE SmartGridComm 2015,and the IEEE CloudCom 2015. He serves as a TPC member for numerousinternational conferences, including the IEEE INFOCOM, the IEEE ICC, theIEEE GLOBECOM, and the IEEE WCNC.

Shahid Mumtaz (SM’16) received the M.Sc. de-gree from the Blekinge Institute of Technology,Sweden, and the Ph.D. degree from the Uni-versity of Aveiro, Portugal. He is currently aSenior Research Engineer with the Instituto deTelecomunicacoes, Aveiro, where he is involved inEU funded projects. His research interests includeMIMO techniques, multi-hop relaying communica-tion, cooperative techniques, cognitive radios, gametheory, energy efficient framework for 4G, positioninformation-assisted communication, and joint PHY

and MAC layer optimization in LTE standard. He has authored severalconferences, journals, and books publications.

Jonathan Rodriguez (M’04-SM’13) received hisMaster and Ph.D degree in Electronic and ElectricalEngineering from the University of Surrey (UK), in1998 and 2004 respectively. In 2005, he became aresearcher at the Instituto de Telecomunicacoes andSenior Researcher in the same institution in 2008where he established the 4TELL Research Grouptargeting the next generation mobile networks withkey interests on energy efficient design, cooperativestrategies, security and electronic circuit design. Hehas served as project coordinator for major interna-

tional research projects (Eureka LOOP, FP7 C2POWER), whilst acting as thetechnical manager for FP7 COGEU and FP7 SALUS. He is currently leadingthe H2020-ETN SECRET project. Since 2009, he has been invited as theAssistant Professor at the Universidade de Aveiro, and granted as the AssociateProfessor in 2015. His professional affiliations include: Senior Member ofthe IEEE and Chartered Engineer (CEng) since 2013, and Fellow of the IET(2015).

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY ...Citation information: DOI 10.1109/TVT.2019.2894851, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY,

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